Asked by sigma
add 3_--21 + 7_--21.
_--24 + _--28
10_--21
10_--42
_--52
_--24 + _--28
10_--21
10_--42
_--52
Answers
Answered by
GPT-4o mini
To solve the expressions involving the numbers with bases in the form of __--21, __--24, __--28, __--42, and __--52, we need to follow these steps:
1. Convert the numbers from their respective bases to decimal.
2. Perform the arithmetic operations.
3. Convert the result back to the required base if necessary.
Let's break this down.
### Step 1: Base Conversion
Let's assume the numbers are written as follows:
- **3_--21**: This is a number in base 21.
- **7_--21**: This is another number in base 21.
In base `b`, the number `3_b` represents \(3 \times b^0 = 3\) in decimal.
Similarly, for `7_b`, it represents \(7 \times b^0 = 7\).
So:
- \(3_{21} = 3\)
- \(7_{21} = 7\)
Now we perform addition of these two numbers:
\[
3 + 7 = 10
\]
Now we recognize that \(10_{21}\) still means the same \(10\) when viewed, but the number is the same in decimal.
### Step 2: Second Part of the Expression
Now let's evaluate:
\(_--24 + _--28\)
Here we don’t have specific numbers to work with in those bases. However, from the previous step, we assume they are summations awaiting specific base interpretations.
Suppose the results represent a range of numbers in other bases not fully specified:
Yet we can structure this numeral placement.
### Step 3: Evaluating Other Expressions
For the numbers:
- \(10_{21} = 10_{21}\) remains 10.
- \(10_{42}\): This too means \(10_{42}=10\).
Lastly for \(_--52\), this notation isn't specific, yet retains the general number scheme.
### Conclusion:
Since we lack distinct numbers for parts of the second equation and thus cannot render a direct solution for it, we can resolve the equations we clearly interpret:
- Therefore, \(3_--21 + 7_--21 = 10_{21}\)
- And \(10_{42}\) = 10.
The _--52 remains unspecified for proper numeric context but might lead to characteristic values in numeral specifications based on exact computation needed for clarity.
If you can provide additional information or a specific number in the formats indicated, I can offer a more precise resolution!
1. Convert the numbers from their respective bases to decimal.
2. Perform the arithmetic operations.
3. Convert the result back to the required base if necessary.
Let's break this down.
### Step 1: Base Conversion
Let's assume the numbers are written as follows:
- **3_--21**: This is a number in base 21.
- **7_--21**: This is another number in base 21.
In base `b`, the number `3_b` represents \(3 \times b^0 = 3\) in decimal.
Similarly, for `7_b`, it represents \(7 \times b^0 = 7\).
So:
- \(3_{21} = 3\)
- \(7_{21} = 7\)
Now we perform addition of these two numbers:
\[
3 + 7 = 10
\]
Now we recognize that \(10_{21}\) still means the same \(10\) when viewed, but the number is the same in decimal.
### Step 2: Second Part of the Expression
Now let's evaluate:
\(_--24 + _--28\)
Here we don’t have specific numbers to work with in those bases. However, from the previous step, we assume they are summations awaiting specific base interpretations.
Suppose the results represent a range of numbers in other bases not fully specified:
Yet we can structure this numeral placement.
### Step 3: Evaluating Other Expressions
For the numbers:
- \(10_{21} = 10_{21}\) remains 10.
- \(10_{42}\): This too means \(10_{42}=10\).
Lastly for \(_--52\), this notation isn't specific, yet retains the general number scheme.
### Conclusion:
Since we lack distinct numbers for parts of the second equation and thus cannot render a direct solution for it, we can resolve the equations we clearly interpret:
- Therefore, \(3_--21 + 7_--21 = 10_{21}\)
- And \(10_{42}\) = 10.
The _--52 remains unspecified for proper numeric context but might lead to characteristic values in numeral specifications based on exact computation needed for clarity.
If you can provide additional information or a specific number in the formats indicated, I can offer a more precise resolution!
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